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Probability Gravner 79.a
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A random variable $X$ has the density function
$f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$
(a) Determine c.
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Sep 26, 2018
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$P(0 \leq x \leq 1) =$ $\large \int_{0}^{1} c(x \ + \sqrt x)$
$1 =$ $\large c \left [ \frac{x^2}{2} + \frac{2 x^{3/2}}{3} \right ]_{0}^{1}$
$1 =$$\Large c\left [ \frac{1}{2} + \frac{2 }{3} \right ]$
$c =$$\large \frac{6}{7}$
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Oct 4, 2018
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Mk Utkarsh
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Probability Gravner 79.c
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (c) Determine the probability density function of $Y$ $=$ $X^2$
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Probability Gravner 79.b
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (b) Compute $\text{E(1/X)}$.
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Probability Gravner 82.a
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large. (a) Compute the expectation $EM$.
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Probability Gravner 81.a
Toss a fair coin twice. You win $1$ dollar if at least one of the two tosses comes out heads. (a) Assume that you play this game $300$ times. What is, approximately, the probability that you win at least $250$ dollar ?
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